Context - A Real Court CaseIn the early 1970s, a young man challenged an Oklahoma state law that prohibited the sale of 3.2% beer to males under age 21 but allowed its sale to females in the same age group. The case (Craig v. Boren, 429 U.S. 190, 1976) was ultimately heard by the U.S. Supreme Court. The state of Oklahoma argued that the law improved traffic safety. One of the three main pieces of data presented to the court was the result of a “random roadside survey.” This survey gathered information on gender and whether or not the driver had been drinking alcohol in the previous 2 hours. A total of 619 drivers under 21 years of age were included in the survey.PromptA test of independence may be appropriate if we are examining the relationship between two categorical variables in one population. For this situation what is the population? What is the explanatory variable? What is the response variable?What are the hypotheses for the Test of Independence? State hypotheses with reference to the context of the scenario.The spreadsheet of the data looked like this: Roadside survey dataDriverGenderAlcohol in lasttwo hours?Driver 1MYesDriver 2FNoDriver 3FYes.........Driver 619MNo We will not use the raw data. Instead we will use the summarized data shown in the table below. Roadside survey summaryDrank alcohol in last 2 hours?YesNoTotals Male77404481 Female16122138 Totals93526619Use StatCrunch to find expected counts, the Chi-square test statistic and the P-value. (directions) Copy and paste your StatCrunch table into your post. How many males in the sample are expected to answer yes to question about alcohol consumption in the last two hours? Show how to calculate this expected count and explain what it means relative to the hypotheses.Explain how we know that this data meets the conditions for use of a chi-square distribution.State a conclusion at a 5% level of significance. Do you think that the data supports the Oklahoma law that forbids sale of 3.2% beer to males and permits it to females?

Choose two of the arguments below and write a direct proof using the eight rules of inference introduced in section 8.1 of the textbook. You can do argument 1 or argument 2, but not both, then any of arguments 3–6. Note that commas are used to separate the premises from each other.1. ~M, (~M • ~N) → (Q → P), P → R, ~N, therefore, Q → R2. ~F → ~G, P → ~Q, ~F v P, (~G v ~Q) → (L • M), therefore, L3. ~(Z v Y) → ~W, ~U → ~(Z v Y), (~U → ~W) → (T → S), S → (R v P), [T → (RvP)] → [(~R v K) • ~K], therefore, ~K4. (S v U) • ~U, S → [T • (F v G)], [T v (J • P)] → (~B • E), therefore, S • ~B5. ~X → (~Y → ~Z), X v (W → U), ~Y v W, ~X • T, (~Z v U) → ~S, therefore, (R v ~S) • T6. (C → Q) • (~L → ~R), (S → C) • (~N → ~L), ~Q • J, ~Q → (S v ~N), therefore, ~RNatural deduction is so called because it is a model for how we naturally reason. This often comes as a surprise to students because all of the symbols seem anything but natural. The symbols, however, allow us to focus on the form of the argument without getting bogged down by content. Recall that each sentence letter represents a simple sentence in English.After writing your direct proofs, construct a translation key for your argument by assigning each letter a simple sentence, and use that key to fill in the content of the argument.